Is the equation x⁹ - 5x³ + 6 = 0 quadratic in form? Explain why or why not.

Solution:

An equation where the highest exponent of the variable (usually "x") is 2. It can be x² but no x³.

In other words, a quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

A Quadratic Equation is usually written as ax² + bx + c = 0.

Where a,b and c are constants

x = unknown variable

Example: 8x² + 5x - 3 = 0.

Given, the equation is x⁹ - 5x³ + 6 = 0

The exponent of the first term is 9 while that of the second term is 3, the square of 3.

While squaring x³ we get x⁶ instead of x⁹.

Therefore, the given equation is not quadratic in form.

Is the equation x⁹ - 5x³ + 6 = 0 quadratic in form? Explain why or why not.

Summary:

The equation x⁹ - 5x³ + 6 = 0 is not in quadratic form.